Modelling of Missile Kinematics with Distance &Missile Speed̖ Time Depended on Moving Object Speed Initiated from Space Random Point

Abstract

The modelling about missile kinetic behavior is going to search the attacked moving object in this study. The speed̖ distance̖ missile speed with needed time could be searched and find some information about it. Firstly that AB distance has been 0.5Km when speed is to be 1 mach in order to hit the moving target with accuracy. In light of checking the speed the actual missile hitting speed which becomes from 0.18Km/s to 1Km/s will be computing to compare with object speed from 0.22Km/s to 1.9Km/s through the method in advance. Secondly when the object speed raises from 100m to 950m with angle f is 40°, b is 40°. It means that time has been 1~1.5 s when speed is to be 1 mach so as to hit the moving target accurately. Correspondingly the attacking time will demand 6s when object speed becomes 0.1Km/s.
Keywords: Modelling; missile kinematics; distance; time; speed; movement’s object; initiated; space random point

Introduction

The missile as an important weapon could be used in defence department. Especially in war period it can play an significant role on modern inter-country’s conflict, therein the corresponding emphasis will be taken in world’s main countries. The missile has been searched in advanced assembly to attack enemy’s device whose meaning is significant from the strategic view. So we must search it and make it to be more aggressive continuously by engineer and scientist for planning new functions to be precision attack which can be put urgent position. In this paper its Kinematics establishment can attack a moving object like ship, flighter, missile etc. which may be establishing simulation equation to analyze its precise problem because the accurate attack may promote its effectiveness. So the research could investigate that factor to look forwards to seeking important message for us to search continuously [1-4]. Through this research the important parameters should be sought and found for making sure the demand from engineer and scientist. For the sake of making low cost weapon like missile the relevant high performance should be cultivated and developed, which has been destination of this paper in brief and concluded in here. We have found the distance and time depended speed relations from the simulating results. In short the missile or plane is able to initiate from space one point to realize the attack destination, which can be simulated here. At the same time the corresponding parameters could be regulated to finish the attack task precisely. The precision will be an important mission in attacking moving target that needs many simulation or practice to prove constantly.

Modeling for missile Kinetics

It is supposed that one object in y axis movement with v speed. We can establish the modelling with below steps for attacking the object in B point whose principle is shown as shown in Figure 1. The A point will be missile starting one while B point is able to attack placement. There qpresents angle in x-z coordinate; fpresents angle in OA and y axis; a presents OA’ resolved by OA in x-y one.

Since OA¢¢=OA¢cosa —(1)

and OA¢=OAcosq —(2)

So OA¢¢=OAcosacosq —(3)

On the other hand

Due to OB=vt —(4)

Since A¢B²=OB²-AA’² —(5)

And AB²=A¢B²+A¢A²  —(6)

And OB²=OA²+AB²-2cosbcosf  —(7)

So it has  —(8)

This equation will be pursuing the moved object distance and angle, OA distance function.

On the other side, since

So it has   —(9)

And   —(10)

These ones (9) will be moving object equation for parameters inferring above.

Here in x-y-z coordinate system A presents x-y-z coordinate system one point and A¢ presents in x-y one while A¢¢ indicates A’ resolution in x axis. At last in y axis there is a moving object with v object speed. The t is the passing time to hit the target object at B point.

Figure 1 The missile attacked kinematic resolution diagram in x-y-z three coordinate.

Figure 2 The relationship between OA and AB distance with f=30°.

Figure 3 The relationship between OA and AB distance with f=25°.

The AB distance is going to enhance from 50m to 570m in Figure 2 when the OA distance raises from 100m to 1,000m with angle f is 30° proportionally. It means that OA distance has been longer than AB distance which is able to the distance to moving target nearly so that it is easily possible. In light of checking the OA distance the actual hitting distance AB will be computing through the method in advance. The ratio will attain 0.57 between OA and AB. Figure 3 has been relationship between OA and AB which shows the lower ration with 0.56 when the angle f is 25°.

Figure 4 The relationship between demanded time and object speed with f=40°, b=40°.

Figure 5 The relationship between AB distance and object speed with f=40°, b=40°.

The demanded time is going to enhance from 6s to 0 in Figure 4 when the object speed raises from 100m to 950m with angle f is 40°, b is 40°. It means that time has been 1~1.5 s when speed is to  be 1 mach in order to hit the moving target with accuracy. In light of checking the speed the actual hitting time will be computing through the method in advance. Figure 5 has been relationship between AB and speed which shows the declining function. The former is about to reduce from 800m to 150m while the object speed enhances from 100m/s to 960m/s accordingly. Additionally the object speed will relate to both the two angles while OA only relates to f.

Figure 6 The relationship between AB distance and object speed with f=40°, b=20°.

Figure 5 The relation of missile attacking time and moving object speed in moving object with three coordinate within b=30°, f=35°.

The AB distance is going to reduce from 800m to 100m in Figure 6 when the object speed raises from 0.1Km to 0.95Km with angle f is 40°, b is 20°. It means that AB distance has been 0.5Km when speed is to be 1 mach in order to hit the moving target with accuracy. In light of checking the speed the actual missile hitting speed which becomes from 0.18Km/s to 1Km/s will be computing to compare with object speed from 0.22Km/s to 1.9Km/s through the method in advance. Figure 7 has been relationship between AB and OA shows the inclining function. The former is about to enhance from 0.15Km to 0.8Km while the latter enhances from 0.18Km to 1.25Km accordingly.

Figure 7 The relationship between missile AB distance and object OA distance with f=40°, b=20°.

In short those parameters would have been computed in this paper in order to evaluate the performance for attacking the moving target accurately. The OA, AB, missile speed and moving time depended speed is able to be solved through this study. The five parameters can be clarified to attack a moving object. So the AB will be linear relationship with OA which is shorter than OA. When the object speed raises from 0.1Km to 0.95Km with angle f is 40°, b is 20°. The distance AB and object speed shows the declining function. The former is about to reduce from 800m to 150m while the object speed enhances from 100m/s to 960m/s accordingly.

Conclusion

That OA distance has been longer than AB distance which is able to the distance to moving target nearly so that it is easily possible. In light of checking the OA distance the actual hitting distance AB will be computing through the method in advance. The ratio will attain 0.57 between OA and AB. Firstly that AB distance has been 0.5Km when speed is to be 1 mach in order to hit the moving target with accuracy. In light of checking the speed the actual missile hitting speed which becomes from 0.18Km/s to 1Km/s will be computing to compare with object speed from 0.22Km/s to 1.9Km/s through the method in advance. Secondly the AB value is going to decrease when the object speed increases which is going to increase from 0.1Km to 0.8Km while object speed enhances from 0.15Km/s to 1.2Km/s that means that the AB with maximum 0.8Km will follow minimum speed 0.1Km/s accordingly. Thirdly the time is going to decrease from 6s to 0 while object speed enhances from o.1Km/s to 1Km/s with f=40°, b=20°. Correspondingly the attacking time will demand from 6s to 0 one when object speed becomes from 0.1Km/s to 1Km/s respectively.

Acknowledgements

This work had been partially sponsored by the KNRF (Korea National Research Foundation), under the Specified Base Program granted No 96-0300-11-01-3.

References

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